A bike originally costs $529.99 and is on sale for $317.99. What was the amount discounted?

A university found that of its students withdraw without completing the introductory statistics course. Assume that students reg

polet [3.4K]

Answer:

A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

a. Compute the probability that 2 or fewer will withdraw (to 4 decimals).

= 0.0355

b. Compute the probability that exactly 4 will withdraw (to 4 decimals).

= 0.1304

c. Compute the probability that more than 3 will withdraw (to 4 decimals).

= 0.8929

d. Compute the expected number of withdrawals.

= 6

Step-by-step explanation:

This is a binomial problem and the formula for binomial is:

$P(X = x) = nCx p^{x} q^{n - x}$

a) Compute the probability that 2 or fewer will withdraw

First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 2) = 20C2(0.3)^2(0.7)^{18}\\P(X = 2) =190 * 0.09 * 0.001628413597\\P(X = 2) = 0.027845872524$

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 1) = 20C1(0.3)^1(0.7)^{19}\\P(X = 1) =20 * 0.3 * 0.001139889518\\P(X = 1) = 0.006839337111$

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 0) = 20C0(0.3)^0(0.7)^{20}\\P(X = 0) =1 * 1 * 0.000797922662\\P(X = 0) = 0.000797922662$

Finally, the probability that 2 or fewer students will withdraw is

$P(X = 2) + P(X = 1) + P(X = 0) \\= 0.027845872524 + 0.006839337111 + 0.000797922662\\= 0.035483132297\\= 0.0355$

b) Compute the probability that exactly 4 will withdraw.

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 4) = 20C4(0.3)^4(0.7)^{16}\\P(X = 4) = 4845 * 0.0081 * 0.003323293056\\P(X = 4) = 0.130420974373\\P(X = 4) = 0.1304$

c) Compute the probability that more than 3 will withdraw

First we will compute the probability that exactly 3 students withdraw, which is given by

$P(X = x) = nCx p^{x} q^{n - x}\\P(X = 3) = 20C3(0.3)^3(0.7)^{17}\\P(X = 3) = 1140 * 0.027 * 0.002326305139\\P(X = 3) = 0.071603672205\\P(X = 3) = 0.0716$

Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1 - 0.1071=0.8929

d) Compute the expected number of withdrawals.

E(X) = 3/10 * 20 = 6

Expected number of withdrawals is the 30% of 20 which is 6.

5 0

3 years ago

F represents the fee (in dollars) for climbing d meters.

Grace [21]

Answer:

$12

Step-by-step explanation:

when d = 0, F = 110

when d = 100, F = 110 + (0.12 x 100) = 122

when d = 200, F = 110 + (0.12 x 200) = 134

etc.

Therefore, increase in price for every 100 meters climbed = 134 - 122 = 122 - 110 = 12

3 0

2 years ago

A number cube is rolled and a coin is flipped.

Mademuasel [1]

Answer:

30

Step-by-step explanation:

5 0

3 years ago

I need help with slope (8th grade)

Triss [41]

Answer:

(y1-y2)/(x1-x2)

Step-by-step explanation:

if you have two points from the graph then you can use them to find the slope, for example:

(2,3) and (0,5)

you would take the first point and put it in a fraction (and the second point) but the x goes on the bottom and the y goes on the top:

3/2 and 5/0

Next you put them together minusing one of the equations, but make sure that the two coordinates line up (it doesn't matter which one, in the order):

3-5/2-0

Then you solve:

-2/2

-1

which means that -1 is the slope for this

(the "/" is a fraction bar, in case you didn't already know that)

5 0

3 years ago

Solve multi-step equations iready<br> -5m=3<br> m=?

gayaneshka [121]

Answer:

m = -3/5

Step-by-step explanation:

-5m = 3

Divide each side by -5

-5m/-5 = 3/-5

m = -3/5

7 0

2 years ago